A STUDY OF NORMAL GALAXIES THROUGH FAR INFRARED SPECTROSCOPY
DISSERTATION Submitted for the award of the degree of Master of Philosophy in PHYSICS
BY SHAFIQULLAH
Under the Supervision of PROF. ABDUL QAIYUM
IHBUHHH DEPARTMENT OF PHYSICS "WHWI LIGARH MUSLIM UNIVERSITY DS3794 ALIGARH (INDIA) 2006 Illilll nS3794 DEPARTMENT OF PHYSICS ALIGARH MUSLIM UNIVERSITY ALIGARH-202002 (U.P) INDIA Phone No.0091-571 -2701001
CERTIFICATE
Certified that the work presented in the M. Phil, dissertation entitled "A STUDY OF NORMAL GALAXIES THROUGH FAR INFRARED SPECTROSCOPY" is the original work of Mr. Shafiqullah, carried out under my supervision.
(Prof. Abdul Qaiyum) Acknowledgements
/ feel honoured in expressing my deepest sense of gratitude to Prof. Abdul Qpiyum, who suggested me this topic and has been a constant source of inspiration; under whose proper guidance I was able to shape out my work. I am indebted to the chairman, Department of Physics for facilitating me with the needs and requirements. I am also thankful to other Teachers of this esteemed Department of Physics for their useful comments and suggestions specially to Mr. Badre Alam and Prof. Rahimullah Khan. I place on record my thanks to Mr. Shakeb Ahmad, Mr. Mohd. Wasi Khan, Mr. Suhail Ahmad Siddiqui, Mr. Dinesh kumar Shukla, Mr. Amit Singh Chauhan, Mubashshir Ahmad Khan and Mr. Arshad Masoodi for their help and suggestions always available to me. My thanks are due to Seminar Library Staff for their cooperation and facilitating me vnth the required books and journals. My thanks are also due to the staff of the office of chairman for providing all necessary help. I am always owed, from my inner core to friends and research scholars of this Department for their suggestions, invaluable cooperation and constant encouragement. It is my pleasant duty to recall with gratitude the everlasting affection and encouragement and all sorts of support, which I have been receiving from my parents.
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SHAFIQULLAH CONTENTS
Contents Page No.
Chapter -I
INTRODUCTION 1
Chapter -II
PHYSICAL AND CHEMICAL PROCESSES 5 2.1 Physical Parameters and Assumptions 5 2.2 Chemical Equilibrium and Abundance Structure 6 23 Heating Processes in the Interstellar Medium 7 2.3.1 Photoionization of Neutral Atoms 7 2.3.2 Gas Grain Collision 8 2.3.3 Cosmic Ray Heating 9 2.3.4 Hydrodynamical Heating 10 2.3.5 Photoelectric Heating 11 2.3.5 (a) Photoelectric Heating by Bakes and Tielens (1994) 13 2.3.5 (b) Photoelectric Heating by Weingartner and Draine (2001) 15 2.3.6 A Comparative Study of Photoelectric Heating Models 20 Chapter - III
LINE EMISSIONS 24 3.1 Theory of Line Emission 24 3.2 Cooling of the Gas Through Line Emission 30 3.3 Cooling Structure ofCII(158^im ), 01(63^tm) and CO 31 3.4 Far-Infrared Fine Structure Line Observations 34
Chapter-IV
FIR CONTINUUM EMISSION 38 4.1 Infrared Emissions From Interstellar Dust and Grains 3 8 4.2 Theoretical Estimates of Temperature of Grains And 39 Thermal Emission 4.3 FIR Continuum Observations 42
Chapter - V
RESULT AND DISCUSSION 45
REFERENCES 54 ABSTRACT
We calculate infrared emission spectra for a range of star light intensities from 1 to 10"* times the local interstellar radiation field using the model of Li and Draine (2001), which consists of a mixture of amorphous silicate and carbonaceous grains, each with a wide size distribution in which 60 x 10"* of C (relative to H) is locked up in PAHs. This is presented in the empirical form of average dust temperature and infrared emission flux. The same model of grains is adopted for photoelectric heating of the gas using the formalism of Weingartner and Draine (2001)(hereinafter referred as WD) and Bakes and Tielens (1994)(hereinafter referred as BT). We present an analysis of the cooling lines (^^3/2 ^^^1/2) of singly ionized carbon, [CII], at 15Sjum and (^Pj "^•^^i) of neutral oxygen, [01], at 63//w and far-infrared (FIR) continuum for a variety of star forming galaxies. It has been shown that these radiations are correlated to a large extent. Further line and continuum radiations are used as diagnostics to infer physical conditions in the gas, such as density, radiation fields and abundances. The ratio F^(60/m)/F^(\00^ yields far UV flux Go which is almost same as found from line radiations. It has also been shown that WD model of heating gives better results for a variety of physical conditions but in the region of large Go/ne where grains are more positively charged BT model fits the observation better than WD because of high sticking coefficient of electrons. CHAPTER -1
INTRODUCTION Before 1930, it was general perception among astrophysicistjthat the vast space between the galaxies and stars are empty and light can propagate indefinitely in the space without extinction. It was Robert Trumpler (1930) whose discovery of colour excess provided the first definitive proof of the existence of matter between stars. These were termed as Interstellar Matter (hereafter referred as ISM). Thus hypothesis of completely empty space was not found to be true and the material that causes extinction in light was proposed as" Dust Grains". These dust grains are the components of the interstellar medium which play an important role in absorbing the light coming fi-om stars and then emit these absorbed light in the form of radiation in X-ray, infrared and radio regions. Definitely hydrogen gas makes up most of the interstellar matter, but essentially all of the chemical elements occur in the interstellar mediimi. About 90% of the atoms in the space are hydrogen with 9% helium and rest 1 percent consists of all other elements. So far as dust grains in the ISM are concerned they constitute very small fraction by number but by mass they are «14 x 10~^^ gm/atom. In spite of the fact that these are small in numbers but they are major source of scattering and absorption of UV radiation from nearby stars. The composition of dust grains varies in interstellar medium. About half of the volume of interstellar dust is made up of silicate grains. The other half has to be in the form of graphite particles or organic reflectory grain mantles. The other compositions of interstellar dust grains are polycyclic aromatic hydrocarbons (PAHs) and amorphous carbon. Some of the dust grains are also in the form of icy grains mantles. Interstellar dust is an important component of interstellar medium. It determines the heating and cooling of the cloud through energetic photoelectron and gas-gas collision. It is also dominant source of opacity and hence determines the spectrum of the dust-enshrouded objects. Molecular hydrogen, the most abundant gas-phase species in molecular cloud is formed on grain surface. Grains can also influence gas-phase composition of molecular clouds indirectly because they may lock up some of the elements. Metals tend to carry the charge inside a dense cloud and thus regulate the ion- molecule chemistry. Apart from that dust grains protect the atoms, ions and molecules from ionization and dissociation by absorbing the UV radiation incident upon the medium/cloud. In the following chapter 2 we discuss the various physical parameters and assumptions that are important for calculation of chemical equilibrium, abundance structure, heating and cooling in the interstellar matter. In this chapter we also discuss the chemical equilibrium that are set up between formation and destruction processes of a particular species to solve for the abundance structure, specially that of neutral and ionized carbon, neutral oxygen, ionized silicon and also some other atomic species and CO molecule at a particular position in the region. To determine the ionization structure, the photoionization by ultraviolet radiation (A > 912 A) fromneares t hot stars, cosmic ray ionization and molecular exchange reactions are considered. In this chapter various heating processes are also discussed through which energy is deposited in the interstellar medium. The interstellar medium in the galaxies is heated, dissociated and ionized by the FUV photons from young stars both near and far. The FUV photons in the energy range 5eV
PHYSICAL AND CHEMICAL PROCESSES
2.1 PHYSICAL PARAMETERS AND ASSUMPTIONS
The penetration of FUV radiation into the diffuse and dense clouds is a sensitive fiinction of the distribution of dust and grain and their sizes in the medium of interest. For the present calculation we consider both graphite and silicate grains. The description of siUcate and graphite grains are given by Li and Draine (2001) and Weingartner and Draine (2001), in which the smallest gains are polycyclic aromatic hydrocarbons (PAHs) molecules and the largest grains consists of graphite, and grains of intermediate size have optical properties intermediate between those of PAHs and graphite. We adopt a plane parallel geometry in which one face is illuminated by FUV radiation and changes in the
mean intensity of FUV radiation is proportional to e~ ' " provided that total visual extinction is large. Here Ay is the visual extinction coefficient and Ky takes care of extinction in UV region at different frequencies. The values of K^ are in the range of 1 to
3.5 for different processes considered here (Qaiyum, 2003). The RV=AV/EB-V, ratio of visual extinction to reddening is taken as 3.1. The standard relationship between column density NH and visual extinction Ay is adopted asA^^ =1.87xlO^'^p,(Bohlin et al., 1978). Further the medium is also supposed to be homogeneous but not isothermal. We adopt the average interstellar radiation field of Habing (1968) as reference field which has the energy density =5.33x10"''* erg cm'^ between 6 and 13.6 eV less by a factor of 1.13 than the energy density 6.07x10'*'* in the solar neighbourhood as estimated by Mezger et al., (1982) and Mathis et al., (1983). Ligalls et al., (2002) have calculated the intensity of interstellar radiation field (ISRF) to be 2.76x10'^ ergs cm'^ s"', which is 27 percent higher the value quoted by Mathis et al., (1983). This is because of inclusion of blackbody spectrum for the radiation hv less than 5.04 eV. The mean FUV radiation, incident on the surface of a source is assumed to be external and strength of FUV field is taken equal to GoFy. The field Fy is due to Habing (1968). Local source of FUV radiation is supposed to be absent. Thus Go is a measure of strength of FUV field. Simply, by varying the value of Go one can take care of the strength of the radiation field of each source. For the purpose of determination of chemical and thermal structure of the medium a chemical and thermal balance is set up at each position of the source. The interstellar and about 100 species of organic and inorganic molecules. The physical and chemical processes and their reaction rates are taken firom Qaiyum (2003). For the purpose of calculation of heating rates and loss of radiation from different sources radiative transfer equation is solved at each position in the cloud. Density, velocity field and Go are taken as fi-eeparameter . Most of the transitions at millimeter and sub-millimeter wavelengths e.g. CI[307 and 609 ^m], CII[158^m], OI[145|am],SiII[35nm] and high rotational transitions of CO molecule are optically thin except OI[63^m] and low lying rotational transitions of CO. hi the light of these observational facts the semi-infinite slab of de Jong et al.,(1980), extensively used in TH model, is not a safe assumption. Therefore, in the present calculation Qaiyum and Ali (2003) formalism is used.
2.2 CHEMICAL EQUILIBRIUM AND ABUNDANCE STRUCTURE Most of the molecules in the interstellar medium are formed through gas- phase reaction but some of these could also be formed efficiently due to gas-grain reactions. However, in our scheme of calculation both the gas-phase and gas-grain reactions are considered. The reaction rates for the various reactions are taken from Qaiyum (2003). More than 100 species have been observed including isotopic species. However, the important physical conditions indicates that only relatively few species needed to be dealt with explicitly. In particular, the thermal balance and chemical evolution of the mediums depend only upon the smaller number of species, which mainly determine the ionization structure, thermal properties and molecular formation in the ISM. The abundances are calculated using the steady state balances: X In these equations P^ and D^ are the production and destruction rates for the species x of density n,(2)at a position z in the medium; «^(z)and n^(z)are the densities of the electron and of ions i of element x at a distance z. All the formation and destruction mechanism are tabulated by Qaiyum (2003).
2.3 HEATING PROCESSES IN THE INTERSTELLAR MEDIUM The line radiations from atoms, ions and molecules have greatly modified our ideas about the interstellar matter and have revealed a large variety of physical conditions in the interstellar medium. That is why low temperature diffuse and dense interstellar clouds have received considerable attention in the last decade. However, identification of important processes responsible for the observed temperature of interstellar gas continue to be one of the major problems in the theory of ISM, though several studies bearing on the thermal structure of atomic and molecular cloud have been carried out (Tielens and HoUenbach, 1985; Wolfire et al., 1990; Kaufinan et al., 1999). For the heat supply here we consider the following processes:
2.3.1 PHOTOIONIZATION OF NEUTRAL ATOMS The photoelectrons from the neutral atoms transfer part of their kinetic energy to the other gas by collision. This is the main heating mechanism in the HII regions. The electrons are produced mainly by ionization of hydrogen. The kinetic energy of the ejected elecfron is KE = hv-e Where hv = energy of the incident radiation field ^ = /? VQ , the ionization potential For a continuous process such as photoionization, with threshold v^oand absorption cross section cr^,, the product species (photoelectrons and ions) carry off an amount of energy /i(v-Vo) which is added to the kinetic energy budget of the gas through subsequent elastic collisions until the motions of energetic product species have been thermalised. In some cases, Vomay be an "effective" threshold for heating rather than the threshold for absorption in order to compensate for excited state products that decay directly by production of photons that escape without adding kinetic energy to the gas. The heating rate is then T^or.,. = «, lG,F^cTM^-yo)dy erg s'^cm'^ (2.3.1) for absorption by species / of density Uj. F^, is the field due to Habing (1968). Go is the flux normalized to the field of Habing (1968). In neutral regions, atomic carbon, for example, can be photoionized at 11.2< hv 2.3.2 GAS GRAIN COLLISION An important heating source in some neutral regions of high density arises fi'om collisions between gas molecules and dust grains that have been heated by the near- infirared radiation field. An atom or molecule that strikes the surface of a grain at temperature Tgr, that comes into thermal equilibrium with that surface, and the re-enters the gas phase, gas gain kinetic energy firomth e grain if Tgr>T, or lose kinetic energy to it if T>Tgr. The rate of heating or cooling depends upon the temperature difference, the fi-equency of collisions, the composition of the gas, the properties of the particular kind of solid, and the propensity of atoms to stick to the surface (Burke and HoUenbach 1983). If it is understood that a negative heating signifies cooling, then f UT V'' r,_^ = "sr"^''sr[^j oc,2K(T^ -T) erg s"' cm"^ (2.3.3) where the average thermal accommodation coefficient a^ « 0.35 for various types of cold grains (Tgr<100K) in molecular gas at T<100K (Burke and HoUenbach 1983). Interstellar extinction measurements suggest that the typical grain abundance and geometrical cross section are Ajg^o-g, wl.5xlO'^'n„ cm'' So that the heating/cooling rate becomes r^_^^2.1x10-''nf,P^\T^-T) ergs-'cm-' (2.3.4) which is 2.8 times larger than expression of Boland and de Jong (1984), owing primarily to differences in adopted grain cross-sectional areas. Total amount of radiant energy involved in heating and cooling the grains tends to be much larger than that involved in heating and cooling the gas, because the efficiency for heating the grains directly is larger than the efficiency for converting radiant energy into kinetic energy in the gas and because the visible and near-infirared photons effective in heating the grains have a larger integrated energy flux than the ultraviolet photons and X-ray photons that are effective in heating the gas directly. This means that the luminosity of cooling radiation from the grain component of the ISM will usually surpass that of the gaseous component. 2.3.3 COSMIC RAY HEATING Galactic cosmic rays (principally protons) represent a potentially large source of energy input into the interstellar medium. Their total energy density is estimated to be O.SeV cm"' (Spitzer 1978). Cosmic ray protons of relatively low energy, say 2-10 MeV, are most effective in ionizing and heating the gas. However, low energy cosmic rays are also most severely affected by interstellar magnetic fields; therefore, although they may be produced in supernova shocks, they seem not to propagate widely through the interstellar medium. The determination of the heating rate due to cosmic rays is very complicated owing to the myriad processes by which the cosmic rays and their secondary ionization products lose energy. The heating efficiency is sensitive to the composition and density of the gas and to degree of its ionization. In a neutral, molecular gas, the mean heating input per primary ionization (including secondary ionization processes) probability lies in the range, 8h =5.7 to 7.3, the higher value applying at densities nfj> 10* cm'^ (Cravens and Dalgamo 1978). Thus the cosmic ray heating rate in a molecular cloud is r «4xl0 -28 ' /> ^h L/r\n(H,)r X ergs'cm'-l™- 3 (2.3.5) 4x10"'' 6eV while that in an atomic cloud of low ionization is r« 3.5x10 -28 n(H ) erg s"' cm"^ (2.3.6) ^4x10-''y Where ^^ is primary ionization rate. 2.3.4 HYDRODYNAMICAL HEATING This is macroscopic heating to the interstellar gas. The effects of ordered motions in shock waves can be obtained from the velocities, sizes, momenta and energies of expanding supernova remnants, stellar wind bubbles, spiral density waves, and etc. More elusive is the influence of turbulent motions. Except in the very most quiescent dark clouds, widths of interstellar spectral lines tend to be measurably larger than the thermal Doppler widths expected for the measured gas temperatures. The injection of energy into the gas by supernova and their remnants has been discussed many times, notably by Cox and Smith (1974), Mckee and Ostriker (1977), and Cox (1979,1981). For example. Cox (1979) has estimated that a typical interstellar cloud of modest density receives a time-averaged input of mechanical heating of the order of r^^^;, «10"^' eg s' cm'. Such estimates are based upon an average supernova rate and energy release in the context of a global description of interstellar medium. If we are concerned with the input of mechanical energy into a particular cloud, we must apply a model for the dissipation of this energy. In general, if there exists a turbulence of velocity Vt on a scale Re equal to the radius of an interstellar region whose mass density /7 = 2.17x10 ^*w^ grams cm^ (including normal abundances of helium and heavier elements), then turbulent heating enters at a rate '^ipc) -1 -3 r,„,,«3.5xio-^«vX -^ ergs'cm^ (2.3.7) \^c J 10 where Vtisinkms' In the specific context of turbulence generated by gravitationally bound condensations of radius R, mass density p and volume filling factor fy that move through a more dilute medium of density po with characteristic velocity v, Falgarone and Puget (1985) estimate a heating rate due to dissipation of turbulence in the dilute medium of -"f^^Y - Yf/vYi/^c erg s"' cm (2.3.8) r...„«2xio ^_j^-^_,j^_ R Within the boundary layer of condensation, the heating rate is expected to scale as r =r ^ lyrb ^ turbfi KP An alternative formulation of turbulent heating of molecular clouds (Boland and de Jong 1984) yields a heating rate ^ a' ^ r..*« 2.7x10 -30 riuT1. 5 erg s'- I cm (2.3.9) 1 + ar' Where a = is a parameter that characterizes both the turbulent velocity and thermal length scale. A collapsing cloud can be heated by compression. As an example, consider gravitational collapse at the firee-fall rate of a fully molecular clod of density UH, temperature T and pressure p. • cllaspe rf' , 2.6x\0'''n'^'T ergs" cm" (2.3.10) 2.3.5 PHOTOELECTRIC HEATING There are four ways in which interstellar gas can be heated through the dust grains. First, FUV radiation pressure will accelerate the grains relative to the gas and produce a viscous heating term due to gas drag. But it is found to be negligibly small as grain acceleration time scale is short compared with other time scale. Second method of energy exchange is due to grain gas interaction. But it is found that gas temperature is 11 greater than dust temperature in the region (Av<5), therefore, energy exchange between grain and gas collision will cool the gas instead of heating. The maximum energy released during the process of H2 molecule formation is 4.5eV. When it is converted into rate of energy transfer to the medium, it is found to be negligibly small. The fourth mechanism of heating of gas by dust grain is through the ejected electrons from the surface of dust grain by FUV field in the energy Tangr\3.6eV > hv > 6.0eV. This mechanism is termed as "Photoelectric Heating". The high-energy limit corresponds to the cut off in FUV radiation field caused by the hydrogen absorption (hv = \3.6eV), while the lower energy limit correspond to the energy needed to free electron from neutral dust grains (/iv-5.5eV), the work fimction of the neutral grain. The ejected electron may carry energy in the range of 0-8eV. Thus only one third of average energy absorbed goes into the kinetic energy of the electron. Apart from that photoemission yield (photoelectron/absorbed photon) is found to be very close to 0.1 (Bakes and Tielens, 1994). Therefore, photoelectric heating efficiency (ratio between the kinetic energy of the photoelectrons available to heat the gas and the FUV energy absorbed by the grains), e is very close to 0.03. However, the rate decrease as the grain becomes positively charged. This heating mechanism is attractive because these photons are so abundant in interstellar space and most of them end up being absorbed by the dust grains. Heating by photoelectric emission from interstellar grains was first considered by Spitzer (1948). It has now been established that in diffuse and dense interstellar clouds (Av<2) the gas is mainly heated by photoelectrons expelled from dust grain by FUV photons (de Jong, 1977; Draine 1978; Bakes and Tielens 1994; Weingartner and Drain 2001; Li and Draine 2001). In order to calculate photoelectric heating rate consistent with the observations, photoelectric emission process and associated grain charging, realistic photoelectron yields, distribution of photoelectron kinetic energies and electron sticking coefficient are very important under different interstellar conditions. All the parameters depend on the grain size, composition and charging state as well as the spectrum of the illuminating radiation. These will not be discussed here in detail. Presently there are two models operating under different conditions (Bakes and Tielens 1994 and Weingartner and Draine 2001). A comparative study of all these two models have been presented as follows: 12 2.3.5 (a) PHOTO ELECTRIC HEATING by Bakes and Tielens (1994) Bakes & Tielens considered mainly Polycyclic Aromatic Hydrocarbon (PAH) materials. Combination and energetic argument leads to the identification of PAH molecules with « 50 C atoms as an important component of the interstellar gas. The abundances of these species are of the order of 10'^, and making them the most abundant interstellar molecules after H2 and CO. In their paper, they investigated the photoelectric heating of the interstellar gas by a size distribution of carbon grains, which extends down to molecular size. They considered that the small grains of radius < 100A absorb a FUV photons, a fraction of absorbed UV photon energy is dissipated by inelastic collision of the exited electron with the carbon atoms in the grain as it scatters through the grain material on its way to the surface. Some is expended to overcome the work function of the grain, and part is required to overcome the coulomb barrier set up by positive charge due to any previous electron ejection. The electrons will emerge from the grain with kinetic energy of the gas via inelastic collisions. The net photoelectric heating rate H(Nc,Z) composed of Nc carbon atoms and possessing charge Z is given by, HiN,,Z) = W;r["<7^,,(N,)Y,^iN,,IP,)B,ivJeff)g(N,JP,)dv (2.3.11) where W is the FUV dilution factor of the incident blackbody radiation field at temperature Teff such that, Pr = (1.6x10-^ Go)/(o-r,;F/.y,) (2.3.12) where Go is the FUV flux normalized to the Habing field for the solar neighbourhood and FFUV is the fraction of the FUV flux contained in the spectrum considered, a^^^ is the photon absorption cross-section, Yjon is the photoelectric ionization yield and g{N^,IP^) = (\/2{hv-IPJ/hv) is the kinetic energy partition fimction. The integration limit v^ is the frequency corresponding to the ionization potential IPz of a grain of charge Z and By is the Planck fimction. For a size distribution of grains n(Nc)dNc, where n(Nc) is the number density of grains with carbon atoms in the range Nc to Nc+ dNc, the photoelectric heating rate is, 13 Tpe = lXH{N,,Z)nN,,Z)n(NJd^, (2.3-13) where f(N^,Z) is the probability of finding a grain composed of N^carbon atom at a certain charge Z. the summation over Z for each value of N^is taken over allowable ionization states and the range over which N^ is integrated runs from the smallest number of carbon atoms N. to the largest N+. The recombination of charged particles with a grain containing N^ carbon atoms removes energy from the gas at a rate C(Nc,Z) and thus the effective heating rate ^( A^^) may be summarized as, nNJ = j;,[HiN„Z)-CiN„Z)]nN„Z)niNJN, (2.3.14) z for the entire grain population from N-to N+, the net heating rate is given by r„^,, r„e. = [^nK) (2.3.15) The photoelectric heating rate depends on the average charge state of the grain through the fraction of the UV photon energy carried away by the electron. The grain charge distribution depends on the ratio of the ionization rate over the recombination rate, which in turn depends on Go/nc and involving the temperature dependence we have The terms cr^j^jl^^./P^and g{N^,Z) of the frequency-dependentintegra l are all dependent on the size of the dust grain considered. The ionization potential is given as, adopting 4.4eV work function for graphite, IP, =4A + (Z+ 1/2)25.1/Nl"eV (2.3.16) Therefore, they have theoretically modeled the gas heating associated with the photoelectric ejection of electrons from PAHs and PAH clusters. They derived a simple analytical expression for the ionization rate and heating rate by grains of given size as a function of the ionization potential. The formula for photoelectric heating by dust grain derived by Baker and Tielens (1994) is given by, ^pho,oeiecMc='^^'"sGon^ crg s"'cm'^ (2.3.17) Here, 14 4.87x10-^ ^ 3.65xl0-^(r/10^r /2318) and A = GoT"^/n^ HH is the total hydrogen number density and Nc is the colunrn density. This equation is for small grains and PAHs and it is valid up to 10''K. 2.3.5 (b) PHOTOELECTRIC HEATING by Weingartner and Draine (2001) Weingartner and Draine (hereinafter referred as WD(2001)) obtained photoelectric gas heating efficiencies as a function of grain size and the relevant ambient conditions. They foimd less heating for dense regions characterized by Rv=3.1. They considered size distribution, which are consistent with the observed extinction in different regions, with either the minimum or maximum permissible population of ultrasmall grains. They also considered the large grains in contrast to Bakes and Tielens (1994). The expressions for photoemission rate given by WD (2001) is given by, J^ =m'l'^dyYQ^,(y)cuJhy+ [yvcr^cujhy (2.3.19) where Qabs is the absorption efficiency, u^ is the radiation energy density per frequency interval, and c is the velocity of light. The second term in the expression is present only when grains are negative charged. Its contribution is negligibly small in most of the situations. The accretion rates are given by J, = «,5, (Z)(8*r/;zw,)"^;zaV(r„#,) (2.3.20) Where Ui is the number density of species /, 5,(Z)is the sticking coefficient, w,is the particle mass, T is the gas temperature, J is the function of r, = akTIq] and ^, = Zelq^. Z is the charge on the grain. The sticking coefficient changes according to the neutral, negatively and positively charged grains. 15 For some calculations, they adopt a blackbody spectrum for the radiation field, with color temperature Tc and dilution factor W, so that U^=AKWB^{T^)IC It is easy to characterize the radiation intensity by G^ = w^^ /w^^,,, where u"^^ is the energy density in radiation field between 6 eV and 13.6 eV and "WIA =5.33X10"*''erg cm'^ is the Habing estimate of the starlight energy density in this range. The radiation is cut-off at 13.6 eV. The total energy density in the ISRF is u=8.64xl0''^ erg cm'^, with "rod =6.07x10"'''erg cm'^ in the 6-23.6 eV interval, a factor °^ 1.13 more than Habing (1968). The spectrum-averaged absorbed efficiency factor is \QabsUydV The photoelectric emission is dependent on ambient conditions, which are characterized by the shape of the radiation spectrum, gas temperature T and one additional parameter depending on the ratio Go/ue, which we take to be Go( VT )/ne. The gas-heating rate per grain due to photoelectric emission is given by, ^pHcoelecMc («) = Z A (2)[Cv («) + K^ («)] (2-3 -22) The contribution from the photoemission of valence electrons is. 16 Where Emm=0 when Z>0, and Emax=hv-hVpet+Emi„. /^C^) is the photoelectric energy distribution. When Z<0, the contribution from photo detachment is given by, Y\,(a)= r dva^,cujhv{hv-hv^, +E^) (2.3.24) Weingartner and Draine (2001) calculated heating rates under variety interstellar conditions and fitted into the form, ^>^oe,e..c = lO-''G,N,F(T,G„n,) (2.3.25) C^+C,T^* where F{J,G^,n^) = -Q T^'-I-' \-\rC^A^'{\-\-C^A^') the values of Co, Ci, C2, C3, C4, C5 and Ce are given in table 1. The parameters A, Go, NH and He have the same meaning as used earlier. It has been shown by the Weingartner and Draine (2001) that gas-grains collision also cool the gas. The gas grain cooling is important when T>10^K. They derived an expression for grain-gas collision as A^ = 10-^*n,iV^r(^»^^'')e^°^^''' ^''"''''^ (2.3.26) here x=lnA The expression is valid for 10^ < ^ < 10^ and 10^ < 7 < 10\ The values of DO, Dl, D2, D3 and D4 are tabulated in table 2. The effective heating rate may now be defined as, ^eff=^pe-^^ (2.3.27) 17 Table 1 Photoelectric Heating Parameters Rv be Ca Rad. C c, c. c. C4 c. C. err h.' se field 3.1 0.0 A BO 5.56 1.82x10' 0.00492 0.03368 0.557 0.666 0.532 0.15 0.75 3.1 2.0 A BO 3.41 4.27 0.03700 0.00569 0.102 0.490 0.669 0.19 0.89 3.1 4.0 A BO 10.59 4.05x10"' 0.01234 0.01391 0.808 0.580 0.573 0.19 0.94 3.1 6.0 A BO 3.66 7.66 0.00661 0.01552 0.094 0.697 0.482 0.20 0.96 4.0 0.0 A BO 4J0 1.79x10"' 0.00572 0.02488 1.026 0.701 0.505 0.15 0.76 4.0 2.0 A BO 5.03 2.27 0.07441 0.00345 0.140 0.412 0.737 0.18 0.92 4.0 4.0 A BO 3.28 4.44 0.00786 0.01219 0.102 0.686 0.500 0.20 0.96 5.5 0.0 A BO 3.67 2.42x10"' 0.07034 0.00360 0.725 0J65 0.814 0.15 0.77 5.5 1.0 A BO 5.45 2.44x10"' 0.09594 0.00225 0.534 0.418 0.758 0.18 0.89 5.5 2.0 A BO 4.87 7.28x10"' 0.00812 0.01969 0.656 0.620 0.534 0.19 0.94 5.5 3.0 A BO 5.93 9.26x10' 0.00675 0.01648 0.417 0.683 0.489 0.20 0.96 4.0 0.0 B BO 4.8S 6.59x10"' 0.00437 0.04234 0.415 0.664 0.508 0.16 0.86 4.0 2.0 B BO 5.97 0.287 0.00736 0.02065 0J02 0.637 0.528 0.18 0.93 4.0 4.0 B BO 7.97 0.175 0.00277 0.03820 0J82 0.771 0.401 0.19 0.96 5.5 0.0 B BO 4.04 0.653 0.11310 0.00259 0.198 0J48 0.809 0.18 0.89 5.5 1.0 B BO 338 0.608 0.00396 0.02568 0.192 0.752 0.439 0.18 0.93 5.5 2.0 B BO 1.10 3J0 0.00941 0.01431 0.087 0.643 0.524 0.20 0.95 5.5 3.0 B BO 3.47 1.77 0.00494 0.01953 0.140 0.723 0.456 0.20 0.97 3.1 0.0 A ISRF 4J5 2.63x10"* 0.00242 0.03003 1.235 0.827 0J99 0.15 0.73 3.1 2.0 A ISRF 4.87 0.948 0.02576 0.00766 0.188 0.490 0.650 0.18 0.88 3.1 4.0 A ISRF 7.41 0.772 0.03895 0.00606 0.239 0.408 0.708 0.19 0.94 3.1 6.0 A ISRF 9J0 0.248 0.00697 0.01848 0.365 0.633 0.509 0.20 0.96 18 Table 2 Coiiisional Cooling Parameters Rv be Case Rad Do D, D2 D3 D4 Err Field 3.1 0.0 A BO 0.4800 1.783 -7.617 1.655 0.06326 0.17 3.1 2.0 A BO 0.5322 1.325 -6.047 1.435 0.05378 0.14 3.1 4.0 A BO 0.4336 2.108 -7.359 1.736 0.06502 0.14 3.1 6.0 A BO 0.4270 2.120 -7.301 1.786 0.06731 0.15 4.0 0.0 A BO 0.5332 1.379 -7.125 1.504 0.05732 0.17 4.0 2.0 A BO 0.445 2.019 -7.755 1.712 0.06424 0.14 4.0 4.0 A BO 0.4847 1.493 -6.109 1.528 0.05751 0.13 5.5 0.0 A BO 0.4184 2.129 -9.082 1.818 0.06943 0.16 5.5 1.0 A BO 0.4981 1.510 -7.237 1.535 0.05777 0.14 5.5 2.0 A BO 0.4851 1.501 -6.775 1.533 0.05762 0.13 5.5 3.0 A BO 0.4948 1.442 -6.377 1.505 0.05645 0.13 4.0 0.0 B BO 0.4568 1.876 -7.810 1.688 0.06412 0.15 4.0 2.0 B BO 0.4597 1.594 -6.675 1.599 0.06094 0.14 4.0 4.0 B BO 0.5155 1.340 -5.791 1.449 0.05411 0.13 5.5 0.0 B BO 0.4360 1.996 -8.372 1.735 0.06572 0.15 5.5 1.0 B BO 0.5140 1.349 -6.676 1.472 0.05536 0.14 5.5 2.0 B BO 0.4633 1.690 -7.158 1.607 0.06055 0.14 5.5 3.0 B BO 0.4677 1.780 -7.173 1.615 0.06027 0.13 3.1 0.0 A ISRF 0.4291 2.406 -8.357 1.714 0.06354 0.15 3.1 2.0 A ISRF 0.5232 1.678 -5.942 1.339 0.04813 0.14 3.1 4.0 A ISRF 0.3959 2.380 -6.554 1.575 0.05674 0.13 3.1 6.0 A ISRF 0.3632 2.937 -7.601 1.742 0.06228 0.12 19 2.3.6 A COMPARITIVE STUDY OF PHOTOELECTRIC HEATING MODELS: In this section we discuss the resuhs drawn from above given two models for various aspects. Since In^ is good parameter to describe grain charging, so in Figure 1 we show the heating rate as a function of the grain charge parameter GoT° Vn^ for the gas temperature T=100K and plot TIG^NjjiergsQc'^) vs GJ^'^ In^ for various values of Go and electron density ne for the two different models. For increasing GQT'^'^ /«e, the grain charge up and heating efficiency decrease. At this stage, the heating rate proportional to the grain-electron recombination rate. This means the grain-electron recombination rate (and, hence the heating rate) is higher due to Coulomb focusing. However, there are more disks than spheres in the grain distribution, and this more than compensates for the difference in the recombination rate per garin. For low G^T^^ In^ and hence neutral grains, total heating rate is maximum, and there is an approximate agreement among the models, and scales linearly with the intensity of the incident UV field. For high G^T^^ In^, the total heating rate is independent of the intensity of the incident UV field and scales with the product ne and NH. At this point, most of the grains are positively charged, and total heating rate becomes proportional to the electron and electron-grain recombination rate. Bakes-Tielens adopted lager electron sticking coefficients than the Weingartner and Draine and, therefore their curve lies above the Weingartner-Draine's curve. As we have already mentioned that the heating rate increases with gas temperature. This reflects an increase in the grain-electron recombination rate with increasing temperature at those at high gas temperatures. The Coulomb focusing effect becomes negligible. At higher temperatures, the grains become more highly negatively charged with increase gas temperature. This results in a decrease in the photoelectric heating rate. hi Figure 2 we present the photoelectric heating efficiency i.e. fraction of the incident FUV energy deposited in the interstellar medium after ejection of electron from the surface of dust grains. This is shown as a ftmction of hifrared radiations IFIR which is proportional to Go . It is quite clear fromth e graph that photoelectric heating efficiency is 20 high at low Go because of the grains are less positive charged and electrons are ejected with more energy. For high value of Go the grains are highly positively charged due to which Photoelectric efficiency is low. Further it can be seen from the Figure 2 that efficiency for WD (2001) is lower the BT (1994) because of smaller sticking coefficient used. Using realistic grain size distribution WD calculated the net gas-heating rate for various interstellar environments. Study suggests less heating for dense regions characterized by Ry(= Ay/Eg_y) = 5.5 than for diffuse regions v^th Rv=3.1. Photoelectric yields are enhanced for small grain, the net photoelectric heating in interstellar gas are sensitive to the adopted grain size distribution, which should be consistent with the observed extinction curve (which shows strong regional variation). 21 WD (2001) BT(1994) \^^ •.. CO 7 -^ O o 0 I-f -2 -3 G„T"=/N,(l^'^cm') Figure 1. The photoelectric heating rate r per hydrogen total density for average interstellar radiationfield of Habing (1968) 22 0.04 WD (2001) BT(1994) 0.03 c 0) g LU O) I 002 o +-• (D Bo Q. 0.01 -2 -1 Log (lFiR(ergs cm-'2 s-1 "sf) -1, ) Figure 2. Photoelectric Heating Efficiency at N=104 (c, m-3 ), 23 CHAPTER- III LINE EMISSION 3.1 THEORY OF LINE EMISSION: Radiative transfer plays an important role in the problems related with photo dissociation regions and the HII regions, where an energy transport by radiation may determine the structure of the atmosphere, has shown need for methods that yield the net radiative loss due to transition of some species of atoms, ions and molecules. Recent observational studies of FIR and sub millimeter transitions show that most of these lines are optically thin except 01 (63//w) and few low lying rotational transitions of CO. In the light of these observational facts the optically thick (semi-infinite slab) assumption of de Jong et al. (1980), extensively used in TH models to calculate the escape probability is not a safe approximation. In order to meet these observational facts the escape probability formalism should include the escape of photons firom both sides of the slab. For this purpose the radiative transfer equation in a plane parallel slab and isotropic source for distance z and normal to the plane can be written as ;Uc//,/c/r, =0,(x)[/,(r„//)-5,(r,)] (3.1) The solution of the transfer equation depends upon the boundary conditions. Two problems of fundamental importance in Astrophysics are those of a finite slab of material, or a medium (e.g. stellar atmosphere) that has a boimdaiy on one side but is so thick on the other side that it can be imagined to as extending to infinity- semi- infinite atmosphere. For the finite slab problem, we may specify a total geometrical thickness z and optical thickness r^. Following the convention, the optical depth is taken to run fi-om 0 to T^, away fi-omobserve r while the geometrical depth scale runs from 0 to z towards the observer. O^, is the line profile at fi-equency v. To obtain a unique solution of the transfer equation, we must specify the incident radiation field on both faces of the slab. 24 Measuring 6 to be positive away from the observer,// = Cos6 will be greater than zero for pencils of radiation moving towards the observer and less than zero for pencils moving away. Thus we specify the boimdary functions f and g a^ th^'iit . For -l Before writing the formal solution of the equation of transfer it is constructive to consider a few examples; (a) Suppose no material is present. Then ^^ (absorption coefficient) and y^, (emission coefficient) both are zero. This result is consistent with the well-known principle of the invariance of specific intensity when no sources or sinks are present. (b) Suppose that emitting material is present but there is no opacity at the frequency under consideration, then HdIJdt^=j^ (3.5) And for a finite slab emergent intensity is given by the expression, z 7,(0,//) = \ln\j,{z)dz + /,(r,z) (3.6) 0 This expression is of interest physically in the formation of optically forbidden lines in nebulae, hi such lines atoms are excited to metastable levels by collisions, and subsequently some of these decay and emit a photon. The absorption probability for 25 such a forbidden transition is negligible compared with other processes that are depopulating the lower level. Thus, in effect, photons are created at the expense of thermal energy pool of the gas, but none are destroyed by absorption. This situation incidentally is far from LTE. (c) Suppose that there is absorption of radiation in he medium but no emission, then, dl,=-kj,dzln (3.7) And again for a finitesla b the emergent radiation is given by the expression, /(0,//) = /,(r,//)exp(-l///j^,d^) 0 = /,(r,//)exp(-7,///) (3.8) Eqiiation (3.8) is of relevance physically when photons absorbed in the material are converted into photons of another frequency before being reemitted or are destroyed and converted directly to the kinetic energy of the particles in the absorbing medium. Mathematically the radiative transfer equation (3.1) is a linear first order differential equation with constant coefficients. Its general solution will contain all the ingredients discussed above. The equation can be solved in the following way. Suppressing the subscript in equation (3.1) for convenience, we have //^ = (D(/-;y) (3.9) dr or //— = 0/-0.s (3.10) dr The above differential equation must have an integrating factor, namely exp^x/^), thus —[/exp(-TO///)] =-5 exp(-ra)///) (3.11) so that dt, l;f/exp(-TO///) = -_[ 5(0exp(-/(I)///)O—I (3.12) M or /(T,,//) = /(z-2,//)exp[(T, -T^)Q>I^]+ ^'5(0exp[-(/-r,)O///]—C// (3.13) 26 For example, suppose we set TI=0 and take the limit as TJ ^ oo; thus we compute the emergent intensity of a semi-infinite atmosphere. Then by virtue of equation (3.4) 7(0,//)= rs(t)exp(-tO//i)—dt (3.14) * ju Physically this merely states that the emergent intensity is given by a weighted mean over the source function - The weighing factor corresponds to the source from each element of optical depth. As second example, consider a finite slab of thickness T within which s is constant and upon which there is no incident radiation. Then the normally emergent radiation is, / = 5(l-exp(-r)) (3.15) For T » 1, I = s. This is reasonable physically since the energy that emerges should consist of those photons emitted over the mean free path for escape. The rate of emission is /y and mean fi-ee path is \/kp,so it is reasonable that the intensity saturates to s = j/k. For T « 1, exp(-T) « 1-T. So I = sT, here again the answer is sensible physically because in optically thin case we can see through the entire volume. Thus the energy emitted (per xmit area) must be emissivity j times the total path length z through the volume so I = jz = (j/k)(kz) = sT, in this limit we have recovered the equation (3.6). Suppose now we consider an arbitrary interior point in an atmosphere of finite thickness T and apply the usual boundary conditions. Thus considering first the case of \i > 0 i.e. outgoing radiation towards the observer, we have from equation (3.13) O r(T,fi) = + ^s(t)exp -it-T) —dt (3.17) Considering now// < 0 i.e. radiation away fi-om observer, we take r, ^ 0 so that. O. / (T,-//) = /(0,-//)exp(-r—)+ fexp -(T-t)- —dt // * (0 27 or jfrom boundary condition(3.2) /-(r,-//) = +j5(/)exp -iT-t)- —dt (3.19) Equation (3.17) and (3.19) constitute the complete solution of the transfer equation if the source function S(T) is given. After having obtained a formal solution of the transfer equation, we may now perform integration over the angles to derive the specific intensity and to write the solution in a concise and useful form for escape probability formalism. Making use of solution in equation (3.18) and (3.19) for more general purpose, we have, 7(T) = l/2£/(T,/"W>" = 1/2 ([/^(r,//)exp{-(r-T)—}+ (s(t)exp{-iT-T)—}—dt]dju *> ju * fi ^ +1 /2 f [/-(0,-//)exp(-r—) + [s(t)exp{-(r-t)—}—dtW (3.20) •'•1 M MM Since t and // are independent variables, we can change the order of integration in the second term of parentheses. Putting w = 1 /// so that dw dw .,r ^ = — , We get JU W y(r) = i/^(r,/^) rexp{->v(r-T) 1 _ (K> (^ \ F I* dw + -I (0,-ju)\ exp-(wzO}-^+-I s(OOaf/ exp{-w(T-0^— 2 •• w 2 * J w (3.21) The integrals against w are of a well-known form and are called the exponential integrals. In general, for integer value of n, one defines the n* exponential integral by the expression, E„ix) = J°exp(-x///") = x"-^ ^exp(-t/t")dt (3.22) Thus in terms of Ei (x) and E2 (x) equation (2-21) may be written as. 28 y(r) = \l2r(T, n)E, {{T - r)0] +1 / 20 [ s{t)E, [{t - T)<^\dt + \lir (0-^)E^ (zO) +1 / 20 _^ s{t)El[{T - t)<:>]dt (3.23) Now reintroducing the frequency subscript, equation (3.22) may be written as, and replacing I'^{T,ju)andr(0,-ju)hy /^(r^)and 7^(0) respectively, we have, 7;(rJ = l/2/,(Tj£,[(r,-T,)(D,(:c)] + l/2/,(0)£,[(r,O,(x))] + \/2O,ix)ls,it)E,[iT,-t)O^(x)]dt+l/20,(x)[s,{t)E,[{t-Tj(^^ix)] (3.23) Now the profile fiinction can be normalized as follows, rO,(x)dx = l (3.24) J-00 Using equation (3.24), (3.23) takes the form, + ^I,iO)iy^ix)E,[(T, -t)0^{x)]dx + ^ls,it)dtiyi(x)E,[iT^ -t)0,{x)]dx + ^[\it)dtiyiE,[(t,-T^)i^,(x)yt (3.25) Combining the two integrals over t and writing the equation (3.25) in terms of kernel functions ki and k2 defined by Averett and Hummer (1965). MT,) = \/2I^(0)k,M + \/2I,(T^)k,(T^ -Z-J+ [k,[absiT^ -t)\s,{t)dt (3.26) Where, k,[abs{r, -0] = \l2^y^{x)E,[^^{x)abs{r, -t)]dx (3.27) and, k2(K) = £0Ax)E2[^AxK]dx (3.28) Equation (3.26) is the general solution for the local radiation field, which can be used in either condition. Using the properties of exponential integrals one can write. 29 l''k,(T,-t)dt = \-l/2k,M-\/2k,(T,-T,) (3.29) Although in reality the homogeneous and isothermal clouds do not exist but this assumption will simplify the equation (3.26) as, JyM = ^MIAO) + /i(t^-T,)I^M + s^(T,)[l-fiM-^{T^-T^)] (3.30) Where fi(T^,) = —k2(T^,). This is defined, as the probability that a photon emitted at r^ will escape the boundary. As observationally has been found that most of the lines are optically thin therefore the assumption in TH model that total optical depth Ty being oo is contrary to the observations. If T^, -> oo, the equation (2.30) reduces to, JyM = IA0)J3M + sJl- fiiv^)] (3.31) This is the expression used by de Jong et. al. (1980) And Tielens and Hollenbach (1985), Thus in reality, the expression (J.31) should not be employed for the interpretation of observed line intensities from PDRs or diffuse clouds when the lines are optically thin. 3.2 COOLING OF THE GAS THROUGH LINE EMISSION The gas is generally cooled by hyperfine transitions of atoms, ions and rotational transitions of some of the molecules and its isotopes. The cooling efficiency is the function of level populations of different levels, which enter, in the cooling efficiency through the escape probability terms. To solve for level populations, statistical equilibrium for boimd-bound levels m and n are established as: N„ix)(^P,„ix)) = f^N,(x)P,Jx) Forlorn (3.32) /=i /=i Where A^„(x) is the number density of the species x in level/wand P,„ix) is the rate coefficient for the species x between levels 1 and m as: P,n,=B,J,+C,„ (m + K,J.+C„, (ni>l) (3.34) 30 Here A and B are Einsteins A and B coefficients for m and / transitions which corresponds to frequency v and Cim and Cmi are the coUisional excitation and deexication rates. The intensity of radiation Jv is given by the expression as; + P(j^)TtB{y,T,) + P{t,-T,)rtB{v,T,) (3.35) 5„, = 2hvl, /ic\g„N, lg,N„ -1)) (3.36) Here Biy,!^) is the infrared radiation at frequency vand temperature To, r^ is the optical depth at frequency v due to dust. Now the cooling efficiency in units of erg cm' sec" will become as B{v,T,)l3{rS ^ml =Nm^mlhy„lPml 1-- (3.37) PZS,ml here, in the limit /^ -> <» equation (2.37) is reduced to B{y,T,) A„, =iV„^o„,/iv„,/?(rJ 1 (3.38) 'ml This is the same as equation 20 of de Jong et al., (1980) used by Tielens and HoUenbach (1985 ). 3.3 COOLING STRUCTURE OF CII(158//w), OI(63//m) AND CO In the Figure 4- heating and cooling has been plotted as a function of visual extinction (Ay). It is established from the Figure that in the interstellar medium {A^ < 2) the gas is mainly heated by Photoelectric heating by FUV photons and the main coolant are C//(158//w) hyperfme transition ( ^P^^ ->^ P^^) and 01 (63/^) ^P^^^P^) being the next most important coolant. Although region of both the elements are same, therefore, the the beam filling factor the medium during observations will be almost same, although total intensity of the CII line being greater than that of OI. In the interior of the cloud the main coolant is CO molecule. In the Figure 4 it has been shown that contribution to cooling due to CII{l5Sjum) hyperfine transition ( ^^3/2^^^1/2) 31 100 G„=10 Go=io; - - - G„=10' --G„=io; - G„=10^ 3 4 o5 Log(Hydrogen Density (cm") Figure 3. Percentage of Photoelectric Heating Radiated Away as a Cll (158|im)Line Emission 32 -19 h CO I E o W -21 h O) 1- (D C Q -23 h 12 3 4 Ay (Visual Extinction) Figure 4. Photoelectric Heating and Cooling due to Line Emissions of CM, OI(63jim) and CO(J=1-0) for Hydrogen Density = 10^^(001"^) and G^ = 10"* 33 decreases and it is reduced dramatically as the FUV flux from the nearby source is increasing. This is because of the fact that increase of flux ensures more and more heating as a result higher temperature, hi such circumstances contribution of 01 (63//m) (3p^_^3p^^ increase. It is due to the fact that saturation of lines with higher excitation energy occurs at high temperature. 3.4 FAR-INFRARED FINE STRUCTURE LINE OBSERVATIONS In the past two decades, infrared, sub millimeter, and millimeter observations of interstellar medium illimiinated by ultraviolet radiations from nearby stars have revealed moderately strong emissions from fine structure transitions of atoms [CI] 370 and 609 [un, [01] 63 ^un and 145 \xm and ions [CII] 158 ^un, [Nil] 122 |am and [Sill] 35 ^im as well as rotational transitions of CO (AJ=1 up to J=20). Table 3 summarise the properties of these lines. Table 3 Properties of FIR line observed Species Transitions Wavelength T=AE/k Ncr(cm-') (pm) ("K) [CI] ^Pl-^P2 369.87 62.5 3xlo^[H] [CI] ^P.-^Po 609.14 23.6 5xlO^[H] [01] ^P,-^P2 63.18 228 8.5xlO^[H] [oq 'Po-'Pi 145.53 698 lxlO^[H] [cn] 'P3/2-'Pl/2 157.74 92 3xlO^[H] [Nil] 'Pi-'Po 121.89 71 3.1xlO^[e] [CO] J=l-0 2100.73 5.53 3xlO^[H2] [CO] J=2-l 1300.39 16.59 lxlO''[H2] [CO] J=3-2 867.00 33.19 5xlO^[H2] [CO] J=6-5 433.50 116.16 4xlO^[H2] [CO] J=|5-|4 73.62 663.36 8xlO^[H2] 34 These lines are observed towards number of photodissociation regions (PDRs), HII regions, planetary nebulae and reflection nebulae of galactic and extragalactic medium and in high latitude translucent clouds (Tielens and HoUenbach, 1985a,b; Stuzuki et al., 1988;Wolfire et al., 1989;Castets et al., 1990; Tauber and Goldsmith, 1990; Howe et al., 1991; Meixner et al., 1992; Meixner and Tielens, 1993; Robert and Panagi, 1993; Bennet et al., 1994; Steiman-Cameron et al., 1997; Lauhman et al., 1997; Herrmann et al., 1997; Kemper et al., 1999; Jackson and Kramer, 1999; Strozer and HoUenbach, 1999; Habert et al., 2001; higalls et al., 2002; Juvela et al., 2003). Since the available observational data are from variety of conditions, therefore, it is not possible to include all the data for the present analysis. For the present study, we have taken the data of line fluxes for [CII] ISS^m, [01] 63|im and 145|j,m from Malhotra et al.,(2001) for 52 normal galaxies. The data are presented in the Table 4. Table 4 Measured Line Fluxes (in units of 10"*'' W m"^) Galaxy [CII](158nm) [OI](63pn) NGC 0278 0.697 0.312 NGC 520 0.254 0.184 NGC 0693 0.167 0.07 NGC 0695 0.181 0.109 UGC 01449 0.143 0.181 MCG -03-6-01 0.035 0.035 NGC 0986 0.254 0.103 NGC 1022 0.127 0.191 UGC 02238 0.222 0.073 NGC 1155 0.034 0.035 NGC 1156 0.186 0.07 NGC 1222 0.206 0.25 UGC 02519 0.157 <0.059 NGC 1266 0.038 0.054 NGC 1317 0.074 0.041 NGC 1326 0.148 0.076 35 NGC 1385 0.511 0.243 UGC 02855 0.525 0.247 NGC 1482 0.655 0.318 NGC 1546 0.27 0.062 NGC 1569 0.674 0.616 NGC 2388 0.191 0.097 ESO317-G023 0.101 0.068 IRAS F10565+2 0.042 0.076 NGC 3583 0.147 0.088 NGC 3620 0.25 0.164 NGC 3683 0.376 0.17 NGC 3885 0.137 0.11 NGC 3949 0.26 0.183 NGC 4027 0.287 0.148 NGC 4102 0.286 0.268 NGC 4194 0.189 0.243 NGC 4418 <0.028 <0.053 NGC 4490 0.423 0.328 NGC 4691 0.222 0.158 NGC 4713 0.137 0.0185 IC 3908 0.205 0.115 IC 0860 <0.016 <0.025 IC 0883 0.088 0.12 NGC 5433 0.157 0.101 NGC 5713 0.454 0.265 NGC 5866 0.052 <0.029 CGCG 1510.8+0 0.04 <0.02 NGC 5962 0.271 0.083 IC 4595 0.244 0.069 NGC 6286 0.169 0.068 IC 4662 0.094 0.143 NGC 6753 0.288 0.081 NGC 7218 0.18 0.076 IRAS F23365+360 0.017 <0.023 NGC 7771 0.307 0.091 MrK0331 0.137 0.107 36 The observations were taken by the observer using Long Wavelength Spectrometer (LWS; Clegg et al.,1996) on the Infrared Space Observatory (ISO; Kessler et al.,1996), so that a large number of galaxies could be observed at large number of atomic and ionic fine structure lines in the FIR with unprecedented sensitivities. The spectral resolution of LWS was 0.29 and 0.6|xm for wavelength ranges 43-90.5nm and 90.5-197 ^im respectively. 37 CHAPTER IV FIR CONTINUUM EMISSION 4.1 INFRARED EMISSIONS FROM INTERSTELLAR DUST AND GRAINS After the initial detection of 60 and 100|am cirrus emission (Low et al., 1984), Draine and Anderson (1985) calculated the IR emissions fi"omgraphite/silicat e grain with grains as small as 3A and argued that 60 and 100|am emissions could be accounted for. Further processing of IRA.S data revealed stronger than expected 12 and 25|xm emission from interstellar clouds. Weiland et al. (1986) showed that this emission could be explained if very large 3-lOA grains were present. More recent observations have shown that the interstellar medium radiates strongly in emission features at 3.3, 6.2, 7.7, 8.6, 11.3 and 11.9^m. To accoimt for all these features Li and Draine (2001) adopted a dust model which consists of a mixture of amorphous silicate grains and carbonaceous grains, both having a wide size distribution ranging from large grains l^m diameter down to molecules containing tens of atoms in which 60 x 10"* of C (relative to H) is locked up in PAHs. It was assimied that carbonaceous grains have graphitic properties at radii a > 50 A and PAH-like properties at very small size< 20A that accounts for the 3.3, 6.2,7.7 8.6 and 11.3|ani emission features seen in wide range of objects. It has been established by Li and Draine (2001) that thermal equilibrium breakdowns for grains smaller than a 250A, which is heated by individual photons. These small grains get much hotter than the temperature derived by equating the power absorbed with that emitted. The effect is more obvious at short wavelengths (A < 60 |xm). As a result predicted thermal equilibrium 60(im brightness are under estimates of the actual value, while observed dust emissions for /I > 100 A from the interstellar medium can be explained in terms of emissions from big (a > 250 A) silicate and carbonaceous grains and can be obtained from thermal equilibrium brightness. But it has been shown that total FIR emission can be fairly represented by thermal equilibrium brightness. However, from figure 12 and 13 of the Li and Draine (2001) it can be argued that for large FUV interstellar radiation field IR spectra at wavelengths (2 > 60nm) can be safely 38 represented by thermal equilibrium brightness within the observed uncertainty. In the present work for most of the sample galaxies FUV radiation field is expected to be fairly large. Therefore, temperature of spherical grains obtained from the balance of photon absorption and emission will give a representative value of dust emission at /I > 60 jam. 4.2 THEORETICAL ESTIMATES OF TEMPERATURE OF GRAINS AND THERMAL EMISSION The temperature of spherical grain of radius a and material m follows from the balancing photon absorption and emission Am' [G,F,e-''^^''Q^,Mm)dv = An'a' f B,{T^)Q,,,^MMdv (4.1) where By(T,j) is the Planck fimction given by the expression: BATo) = ^^f ,. ).^, , (4.2) c exp{hv/kT,y)-l and TD the grain temperature and QabsA"^^^)is the absorption efficiency for the material m and spherical grain of radius a at frequency v. m=l stands for the silicate grains and 2 for carbonaceous grains. This holds for grain sizes a > 250 A but breaks down for smaller particles, which are stochastically heated (Draine and Li 2001). But it has been argued as well as Ingalls et al., have shown that the equilibrium approach does not affect significantly the conclusion.Q^^^^,(a,w) is approximated as 10"^a(A) and 3xlO"'a(A) for carbonaceous and silicate grains respectively for grain sizes of 10 < a(A) < 1000 in UV range following Weingartner and Draine (2001). The flux of FUV radiations considered here is G^F^, expressed in units of the Habing (1968) flux F^,, which is 1.6x10'^ ergscm'V*. By varying the value of Go we can take care of radiation field for any medium of interest. The grain temperature will also vary with the variation of Go, Following Mathis et al., (1977), we assume a power law distribution of grain sizes: dn„ = C„a-''da, a^ < a < a^ (4.3) where dn„ is the number of grains of type m per H atoms with radii between a and a+da, and the upper and lower size limits of grains are 0.25^m and 0.005|xm, respectively. The 39 coefficients C were determined by Draine and Lee (1984) as 10 "'^cw^' (H atom)' for graphite and 10'" "cm^^ (H atom)'* for silicate grain. Integrating over the grain distribution, the dust thermal emission is K.=I,C„7rrB,(T,)Q^,,^Mm)a-''da (4.4) and intensity integrating fromth e surface of the cloud to Ay is /™(v,Go) = 1.87xlO^'Gof A,.,(^Jci4, (4.5) where dA^ =0.0015Ndr and N is the number density of hydrogen in the photodissociation region and dr is the distance in parsec measured from the surface illuminated by the interstellar radiation field. Total integrated intensity may be obtained using equation (4.5). After considering all the frequencies. To calculate the energy absorbed by the dust grain, we estimate the absorption cross section per hydrogen atom as a fimctiono f wavelength ^>t =^S f""C„a*M(«.'«)«'"«^« (4.6) The energy absorbed by grains may be obtained by integrating over the radiation field: r = '*''L,:„G.f,e-''V,dA (4.7) The wavelength dependent extinction, A;^can be obtained by the integration over the grain distribution: Ax I^H = ZC« l'"T^,,Aa,m)a-''da (4.8) /n where extinction cross section is given by and Qe:.Aa,m) = Q^,,(a,m)/i\-a)) (4.10) The albedo o) = Q^^ IQ^^^ /[I + Q^^ IQabsl- Total emission and absorption by dust grains may be obtained by considering the grains of all size in terms of H atom after integrating 40 over the number of grains of type m per hydrogen atoms with radii between a and a+da of typem. For the present calculation we adopt interstellar radiation field spectrum estimated by Mezger, Mathis and Panagia (1982 and 1983) for hvin electron volts which is expressed as: v[u,(ergcm-')]= (4.11) 3.328x10''(/iv)-^""', U.2 41 graphite grains differ. However, total flux due to emissions from silicate and graphite grain are fitted as a function of wavelength X and parameter To in the following form: FpmW = Co KA''\cxpihc/AkT^)-\)) (4.14) where Co is a constant. Its value depends upon chosen unit of wavelength. The parameter TD is called average dust temperature (representing silicate and graphite together as dust) fitted as a function of Go: 7^=14.796x0°"'' (4.15) The ratio of FIR fluxes in IRAS fllters at 60 and lOOum indicates the average dust temperature in the galaxies. 4.3 FIR CONTINUUM OBSERVATIONS The galaxies in the sample cover the range 0.3-1.37 for F(60pm)/F(100|j,m). The observed continuum fluxes at 60 and 100 /mi and their observed ratios are presented in Table 5 for 52 galaxies. The ratio of FIR fluxes in the IRAS band filters indicates the average dust temperature in the galaxies. The morphology of the galaxies in this sample ranges Irr through E. The galaxies are uniformly distributed across the range of morphological types (see Dale et al. 2000). The FIR luminosity galaxies in this sample range log(LFiR/L0) =7.7-11.2. Since this is study of normal galaxies, we avoided ultraluminous galaxies, which might harbour hidden Active Galactic Nucleis (AGNs). The advantage of the observed continuum emission and their ratio is that they have same beam filling factor. Therefore, for comparison with the theory no estimate of beam filling factor is required. 42 Table 5 CONTINUUM OBSERVATION Galaxy F,(60/mJy) F^i60fm)/F,(lOQfm) FIRilO-'^Wm') NGC 0278 25.05 0.54 139.9 NGC 520 31.1 0.66 160.5 NGC 0693 6.73 0.57 36.75 NGC 0695 7.87 0.58 42.68 UGC 01449 4.96 0.59 26.72 MCG-03-06-01 4.41 1.23 18.85 NGC 0986 25.14 0.49 146.4 NGC 1022 19.83 0.73 98.69 UGC 02238 8.4 0.54 46.91 NGC 1155 2.89 0.58 15.67 NGC 1156 5.24 0.5 30.24 NGC 1222 13.07 0.85 61.86 UGC 02519 2.98 0.4 19.07 NGC 1266 13.32 0.81 64.02 NGC 1317 3.52 0.34 24.49 NGC 1326 8.17 0.59 44.01 NGC 1385 17.13 0.46 103.6 UGC 02855 42.39 0.47 251.4 NGC 1482 33.45 0.72 167.3 NGC 1546 7.21 0.32 51.83 NGC 1569 54.25 0.98 246.1 NGC 2388 17.01 0.68 87.29 ESQ 317-G023 13.5 0.57 73.73 IRAS F10565+2248 12.08 0.79 58.54 NGC 3583 7.08 0.38 46.49 NGC 3620 46.8 0.7 236.4 43 NGC 3683 13.61 0.46 81.52 NGC 3885 11.66 0.71 58.6 NGC 3949 11.28 0.44 68.97 NGC 4027 11.61 0.42 72.57 NGC 4102 48.1 0.68 245.5 NGC 4194 23.81 0.95 109 NGC 4418 43.89 1.37 183 NGC 4490 45.9 0.6 245.6 NGC 4691 14.43 0.62 76.23 NGC 4713 4.6 0.42 28.75 IC 3908 8.09 0.47 47.99 IC 0860 17.93 0.96 81.82 IC 0883 17.01 0.7 85.91 NGC 5433 6.62 0.57 36.15 NGC 5713 21.83 0.57 119.5 NGC 5866 5.21 0.3 38.82 CGCG 1510.8+0725 20.84 0.66 107.5 NGC 5962 8.89 0.4 56.9 IC 4595 7.05 0.39 45.7 NGC 6286 8.22 0.37 54.71 IC4662 8.81 0.74 43.64 NGC 6753 9.77 0.35 66.93 NGC 7218 4.67 0.42 29.19 IRAS F23365+3604 7.44 0.84 35.35 NGC 7771 19.67 0.49 114.5 MrK0331 18.04 0.76 88.55 44 CHAPTER V RESULT AND DISCUSSION In the last two decades DIRBE satellite, Spectrometers aboard IRTS and ISO have made it possible to observe large number of atomic and ionic fine structure lines and continuum in the far infrared, sub-millimeter and millimeter range fi-om interstellar medium in galaxies. As a result, the number of variety of observed interstellar medium of galaxies continue to grow, posing increasingly more complicated challenges to the model computations to determine the physical conditions in the interstellar medium and to interpret the far-infiared and sub-millimeter spectra from galactic and extragalactic sources. In this dissertation we have attempted to xinderstand the energetic and physical conditions in the ISM for statistically representative set of star forming 52 normal galaxies by studying the atomic and ionic fine structure lines in the infi-ared and continuum emissions fi*om dust and grains consisting mixtures of amorphous silicate and carbonaceous grains. The physics of PDRs have been explored using the numerical code of Qaiyum (2005) that contains most up to date values of atomic and molecular data, chemical rate coefficients and grain photoelectric heating rates of Weingartner and Draine (2001) (hereinafter referred as WD) and Bakes and Tielens (1994) (hereinafter referred as BT). Theoretical model proposed here is used in calculating first the dust temperature for silicate and carbonaceous grains and then FIR flux from these grains. The calculated value of dust temperature is fitted in the form as given in equation 4.15. Assuming the grains behave like a black body we calculated the ratio of fluxes for 60 and 100 {/jm) emissions and also the FIR flux. The comparison of the total flux with that of observed provide beam-filling factor of the source, which is utilized for line intensity calculation of the hyperfine transitions of CII[158//w] and 01 [63 fjm]. The observed FIR continuum and line emissions are presented in Tables 4 and 5. Both these radiations are utilized for the study of the physical conditions in the interstellar medium. The calculated ratios of F(60/m)/F(\QOjum) are plotted in the 45 - Fitted Formula o Obsrved Values 0.147 * Calculated Values TD = 14.796XGO ,4.91 FF,R(^) = Co /(r "(exp(hc/XkT,)-1.)) 1.5 E o o E =1 o (D 0.5 1.5 2.5 3.5 Log (G J Fig. 5. Figure shows the variation of the ratio of fluxes at 60 \im and 100 urn : F(60 ^im/lOO ^m) calculated for FIR emissions at thermal equilibrium temperatures of silicate and graphite grains exposed to Interstellar Radiation Field (ISRF) GQ. Continuous line is the ratio obtained from the fitted expressions for average dust temperature Tp and flux F;^. G^ for various galaxies are estimated comparing the calculated and observed F(60 ^m)/F(100 jim). 46 -12.5 o Observed values * Calculated values -12.6 - ¥ * -12.7 * O -12.8 -12.9 -13 0.25 0.5 0.75 1 1.25 1.5 F(60^lm)/F(100^lm) Figure 6. The ratio of 60 ^m to far-infrared continuum, lJ\^^^, is plotted against the ratio of flux in the IRAS 60 and 100 jiim band F(60 )xm)/F(100 ^m). The calculated values corresponding to each source is based on the estimated G„. 47 Figure 5. This figure includes the theoretically calculated ratio of the fluxes as well as obtained from the fitted formula of dust temperature To- From the Figure 5 it is clear that almost all the observed values follow the curve presented here based on the calculated emissions from PAHs and silicate. The values of Go for various galaxies are estimated from the best fit for ratio of flux F(60(xm)/F(100nm) over the whole mentioned range of flux ratios. Further calculated and observed ratios for intensities leo/IpiR at 60/mi and total flux of FIR is presented in Figure 6 for estimated FUV flux Go of various galaxies. It is quite clear from the Figure 5 and 6 that the calculated values and observed values have good agreement for FIR continuum. The estimated parameters Go and number density N are presented in Table 6. The calculated ratio of important cooling lines and far infrared continuum intensities are plotted in Figure 7 for various interstellar radiation field Go, hydrogen density N and carbon abimdances Ac. From the Figure 7 it is clear that for the interstellar medium of galaxies where low electron density and large flux exists, the grains are more positively charged the photoelectric heating due to Bakes and Tielens (1994) give better result because of high electron sticking coefficient, favouring that sticking coefficient used by Weingartner and Draine (2001) should be modified. For higher density and low values of Go photoelectric heating due to Weingartner and Draine (2001) is important. In Figure 8 and 9 ratio of Icn/IpiR and IOI/IFIR for calculated and observed line intensities are compared for the parameters given in the Table 6 which are derived from the observed continuum of the galaxies. It is significant that ratios agree fairly well for 63 as well as 158 (jrni) line emissions of neutral oxygen and ionized carbon. Further Figure 8 and 9 show that line and continuum radiations are tightly correlated, suggesting that contribution to the line and continuum come mainly fromphotodissociatio n regions. 48 -1.5 _p +_ o O) o 4 4.5 Log (Go/N A) Figure 7. The ratio of important cooling lines and far-infrared continuum intensities (heating efficiency) is plotted for various interstellar radiation field G,,, hydrogen density N^ and carbon abundance A^. Filled circles represent the ratio of the observed CM , 01 anf FIR continuum for estimated source parameters Gg, Nf,andAg. Calculated values are obtained for Nf,=100 (cm"^) A^=1.8x10"* and arbitrary G^. 49 f o a> o -3.5 h 0.75 1 F(60^lm/F(100^lm) Figure 8. The ratio of cooling line 158 ^m of [CII] intensity to far-infrared continuum, ICI/IRRV > 's plotted against the observed ratio of flux In the IRAS 60 and 100 |xm band. The calculated ratios are correspondin^j to the source parameters given in the Table . 50 -2 o Observed ratio * Calculated ratio i^ -2.5 C) -3 D) O -3.5 () «? -4 0.25 0.5 0.75 1 1.25 1.5 F(60^lm)/F(100^lm) Figure 9. Calculated and observed ratios of neutral 01 cooling line at 63 ^m are plotted for various galaxies against the ratio of flux in the 60 urn and 100 ^m bands for the source parameters. 51 lAI .E6 Average Physical Parameters Derived by Observed Continuum Emissions Galaxies N(cm-') Log(Go) NGC 0278 176 2.15 NGC 520 132 2.35 NGC 0693 167 2.20 NGC 0695 251 2.25 UGC 01449 309 2.25 MCG-03-6-01 794 3.10 NGC 0986 47 2.10 NGC 1022 91 2.45 UGC 02238 145 2.15 NGC 1155 219 2.25 NGC 1156 200 2.10 NGC 1222 1000 2.65 UGC 02519 166 1.90 NGC 1266 53 2.60 NGC 1317 38 1.75 NGC 1326 158 2.25 NGC 1385 132 2.00 UGC 02855 126 2.05 NGC 1482 295 2.45 NGC 1546 50 1.70 NGC 1569 645 2.80 NGC 2388 120 2.35 ESO317-G023 75 2.20 IRAS Fl 0565+2 63 2.55 52 NGC 3583 71 1.85 NGC 3620 100 2.45 NGC 3683 118 2.00 NGC 3885 224 2.45 NGC 3949 129 1.95 NGC 4027 118 1.95 NGC 4102 59 2.40 NGC 4194 891 2.80 NGC 4418 38 3.15 NGC 4490 141 2.30 NGC 4691 229 2.30 NGC 4713 162 1.95 IC 3908 178 2.05 IC 0860 22 2.30 IC 0883 78 2.45 NGC 5433 276 2.20 NGC 5713 219 2.20 NGC 5866 12 1.65 CGCG 1510.8+0 17 2.35 NGC 5962 78 1.90 IC 4595 74 1.85 NGC 6286 38 1.80 IC 4662 188 2.45 NGC 6753 41 1.75 NGC 7218 141 1.95 IRAS F23365+360 40 2.60 NGC 7771 56 2.05 MrK0331 159 2.50 53 REFRENCES Allen et al., 2004, ApJ, 608,314 Bakes, E.L.O., Helens, A.G.M., 1994, ApJ, 427, 822 Bennet, C.L.,Fixsen,P.J.,Mather,J.C.,Mosley,S.H.,Wright,E.Leplee Jr., R.E., Gales,J.,Hawagama, T., Issacman R.B., Shafer R.A.,Tuipie K.1994,ApJ,434 587 Bohlin,R.C.,Savage,B.D., Drake,J.F., 1987,ApJ,224,132 Boland, W. and de Jong, T. 1984 Astr. 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